Persistent increased breathing results in reduction of carbon dioxide in
the blood, a metabolic waste product that is removed by the lungs. The
build-up of carbon dioxide in the blood is the key signal to the brain
that it is time to breathe, so if it is low, the drive to breathe is
blunted (the lack of oxygen is a much weaker signal, and acts as an
ultimate safety valve). As long as you are awake it isn't much trouble
to consciously breathe, but at night an odd breathing pattern develops
due to a back-and-forth balancing act between these two respiratory
triggers. Periodic breathing consists of cycles of normal breathing
which gradually slows, breath-holding, and a brief recovery period of
accelerated breathing.

This is not altitude sickness

The breath-holding may last up to 10-15 seconds. This is not altitude
sickness. It may improve slightly with acclimatization, but does not
usually resolve until descent.

Periodic breathing can cause a lot of anxiety:

In the person who wakes up during the breath-holding phase and knows he has stopped breathing.

In the person who wakes up in the post-breath-holding hyperventilation (recovery) phase and thinks he's short of breath and has High Altitude Pulmonary Edema (HAPE).

In the person who wakes up and realizes his neighbor has stopped breathing.

In the first two cases waiting a few moments will establish a normal breathing pattern. In the final case, the sleeping neighbor will eventually take a breath, though periodic breathing cycles will likely continue until he or she is awake. If periodic breathing symptoms are troublesome, a medication called acetazolamide may be helpful. Dramatic changes take place in the body's chemistry and fluid balance during acclimatization.

The osmotic center, which detects the concentration of the blood, gets reset so that the blood is more concentrated. This results in an altitude diuresis as the kidneys excrete more fluid. The reason for this reset is not understood, though it has the effect of increasing the hematocrit (concentration of red blood cells) and perhaps improving the blood's oxygen-carrying ability somewhat; it also counteracts the tendency for edema formation. It is normal at altitude to more than usual. If you are not, you may be dehydrated, or you may not be acclimatizing well.